What are you grouping when aligning, also why are you grouping? And what Align To option are you using?
I've tried to replicate the issue (without doing any grouping), and actually discovered something I wasn't aware of that Illustrator CC (2017) does, so I'm wondering if you are seeing a similar behaviour - which in that case would likely be intended:
- I placed a vertical guide
- then aligned the centre anchor point of the point-type (top and bottom text) on that guide as well as the centre of the heart shape.
- After changing the font of the top/bottom text, you'll notice that the text is not properly centred because of the 'spacing' around the various script characters. E.g. the first 'C' is more to the right and the 'e' a the end is almost OFF the baseline.

When I select the top text and heart and use Align to Selection, the top line moves to the left a little and the heart to the right. Which kind of makes sense as that gives a better visual alignment.

You can change the align behaviour by using Align to Key Object:
- Select the objects to align
- Change Align To setting to Align to Key Object.
- Click on the Object to align to (the cursor will change).
- Then click the alignment option

In this case the I selected the heart shape and the top text just moved to the left a bit.