Since you typically round up in Heroclix, I'm assuming you would be able to give 4 actions?

Typically the answer would be 3....

Rulebook p. 7
However, sometimes you may see specialty build rules that also come with scenario specific action totals.

I think this is jumping to a conclusion. If your team is 350 points, that doesn't mean the build total is 350 points.

If the build TOTAL is 350 points, it would be 3 actions (citing the rulebook as above). However, it's not recommended to play at such an odd number. Here's another cite from the rulebook p. 4

So if your team is 350 points, I would assume you're playing a 400 point game and you're just missing 50 points, in which case you would get 4 actions (citing p. 7 above).

Actually, strangely enough, the store I go to has 350 point tournaments. https://www.facebook.com/events/610444285750027/ "Build a team of 350 points or less, using Golden Age rules."