I can't confirm it because I don't have iOS 6 to hand, but I'm pretty sure the difference in button highlights will be the same.
The buttons in Timer works based on the OS wide standard of activating on release.
For a stopwatch, however, you want it to be instant because it's time sensitive. It would kinda suck if you're timings were all out by a bit because you kept you're finger on there slightly too long.
This is actually an example of breaking a convention to improve usability [1]. It's also an example of how if you're looking hard enough you'll find inconsistencies and things that are theoretically horrific in stuff you've been using absolutely fine for years.
The real inconsistency on this screen is that the Reset button doesn't activate on release. If ever there was a time you want to be able to back out of an action by moving your finger away from the button before release I'd say this is it.
While the faux naivity is a bit irritating, it does make a valid point (if not entirely novel). The more you pare back your UI the more you lose distinction between interactive and non-interactive elements. If your buttons are simply color tinted text, it's difficult to unambiguously use color tinting to highlight text of note such as the current day.
What makes iOS 7 really interesting is how it tries to counter that. For example, color hinted text in the edges of the screen will always be actions, so color is enough; color hinted text in the middle of the screen could just be marking interesting things, so actions are usually accompanied by thin borders.
An proper dive into the design and the trade-offs rather than endless "look at this edge-case" would be really interesting.
[1] Caveat because I'm sure otherwise someone will try and pull me up on it. No, this isn't amazing revolutionary design by Apple or super-human attention to detail. I'm sure the Android and WP 7 equivalents work the same.