Change color on modified object

[Hairbrained Scheme]

If I open a black and white graphic png, I can easily pick a color, paint bucket, click, color changed. done.
However, if I modify the image, for example, a low resolution graphic, that I apply blur to smooth, then adjust curves to sharpen, I now have what is an effectively unmodifiable graphic.  So 2 questions.

1. Why in the hell (as I am working with a VERY simple) white on black graphic, selecting blue, then selecting paint bucket, and when clicking on the white in this "modified" state, it turns most of the black to white?  White isn't selected as the color AND I didn't click on the black section of the image?  
My view

2. The only way I have found to be able to accomplish the task needed is to save as PNG and then reopen, and simply choose blue & paint bucket, and single click, done.  Is there a way to "establish" the changes I have made while the file is still open and not have to save as PNG first?
The desired result

[Hairbrained Scheme]

The result of the paint bucket with blue color selected

[Trevor.Dennis]

I am not sure why and how you are using the Paint Bucket, seeing as you are using a Layer Style Color Overlay?  It wouldn't make any difference what colour the object is, as the layer style would cover it.  (FWIIW I suspect that most experience Photoshop hardly ever use the Paint Bucket tool.  The only time I ever use it is to test forum post answers.)

Do you need the black background?  Or are you using PNG to have a transparent background?

Your first screen shot shows the blue object and black background on separate layers.

I see you start by opening an existing PNG file. Does that file have a black background?

I don't know your experience level, so I have to ask, do you realise that image is not a PNG until you save it as such.  In fact if you were to save the layered document as a PNG file and tried to close it, Photoshop would ask you if you wanted to save it again, but using .PSD or .TIFF  Does that make sense?

[Hairbrained Scheme]

Thanks for taking the time here.  

1.  I was using the paint bucket tool since before MS released Windows.  The universal understanding is that all connected pixels of matching color will be instantaneously changed to the new color.  As with much of Adobe, it is these most very basic steps that A. the tool I'm accustomed to suddenly won't work and B. oftentimes the more basic the task, the more research will be required to simply do X.  This turns out to be another great example.  So yeah, the desire was to simply be able to change EITHER the background (paintbucket does this), or the symbol (paintbucket does not).  I understand why you would not use the tool if it does not do what it originally did back in the late 80s.  
2. I use PNG for transparency, yes.  The source is a file someone sent as JPG, and the intent is to send them back an icon (rounded corners) with various color choices.
3. I realize that if I make modifications on layers, I am seeing the top down result.  I still thought that if I modified the only layer referring to a given color, and changed that color, it would reflect through the image (which I still believe it will, if I had been using a method that worked).
So unless you can correct me, the solution to change the symbol color isn't a simple select tool/select color/click, but rather Image Tab / Adjustments / Replace Color / select Drop tool / click on existing color / Click result color square / choose color / OK / OK.  I really hope there is a  simpler way to do this.

[Bojan Živković]

You can try this: select the topmost layer and then press Ctrl+Alt+Shift+E. Use the Paint Bucket tool on the newly created layer. This shortcut will create a merged version of the file without flattening it.

What exactly is your problem? Is it because you have to save and reopen the image or something else?

[Hairbrained Scheme]

This helped simplify things and is a good KS to remember, so thanks.  My problem was trying to change the symbol color.

[Trevor.Dennis]

If you save the attacxhed file  and open in Photoshop, you'll find it has two work paths that smooth out the ragged outline of your screen shot.  The second path, on the right, has taken some ever so slight liberties to tody the outline, but I would have liked to go much further if it was my graphic.  Workpaths are usually the best approach to making shapes like this, and Illustrator the preferred app if you have it (I used Photoshop).

[Hairbrained Scheme]

Nice.  I am familiar with path adjustments in Illustrator but not Photoshop.  Again, thanks for taking the time to assist.

[Conrad_C]

I wonder if this is the problem. See the demo below: The first time I click with the Paint Bucket, I get the same result you do. So I undo that, and the second time, I pay careful attention to what part of the pointer is over the symbol, and I make sure it is the arrow at the top left of the pointer. When I position that over the symbol, it works as expected: The color fills all contiguous pixels of the symbol, not the background.

Now, I do think that is weird. Because I also got it wrong at first. I did expect that it would paint from where the paint bucket is pouring, which is the way the paint bucket has worked in many applications going all the way back to MacPaint in 1984. I did not expect to have to position the arrow instead of the paint drop. I did not know the Paint Bucket pointer in Photoshop now works that way, because like many here, I long ago moved on from the Paint Bucket to the far more flexible and nondestructive ways of coloring. The Paint Bucket is one of the least useful coloring tools at this point, partially because it is still stuck in how digital painting worked in the 1980s. But I ultimately agree that if you do want to use the Paint Bucket tool, its current pointer design in Photoshop is certainly confusing.

One workaround is to press the Caps Lock key, because that puts a painting tool into Precise mode. In that mode you do not see an iconic representation of the tool, only a crosshair. But that helps because the crosshair unambiguously shows you precisely where it is going to paint. (For those who will ask, yes, I did also try setting it to Precise in Photoshop preference settings/Cursors, but guess what, the Painting Cursors settings don’t affect the Paint Bucket, maybe because it isn’t a brush tool? So somehow Caps Lock does let you set it to Precise but the actual Cursors setting does not. Also confusing!)