how can I alter this After Effects CC typing text expression to make time changes???

First, that tutorial is a really lousy one by an enthusiast that gets one thing to work with a really restrictive workflow. The typewriter animation preset does everything that his expression does but it is easier to use, can be easily set to any time, does not depend on the layer in point, can be used with Essential Graphis to create a MOGRT and just plain works. 

The presenter over complicates the expression so you are required to edit the text in the expression. All you need is:

substring(0,time*20)

If you want the animation to start at the layer in-point you need to subtract the inPoint from time like this:

t = time - thisLayer.inPoint;
substring(0, t*20)

To really make it useful you need to add a slider that you can use for speed control, then save it as an animation preset. The expression would look like this:

t = time - thisLayer.inPoint;
spd = effect("Slider Control")("Slider");
substring(0, t*spd)

But that is more work by far and no more useful than using the typewriter text animator that comes with After Effects.  

You have got to vet your trainers. There is a lot more bad advice and poor workflows on YouTube than there is good because it is so easy for the untrained to do a screen recording and pitch their "magic" solution to a specific problem.

Try it this way:

toShow = "John Smith \rHuman Resources"
toShow.substring(0,(time-inPoint)*20)

Dan