I think all 2 1/2 year olds throw tantrums, mine started the minute he turned 2, I think on the night of their birthdays a group of other 2 year olds visit them in the middle of the night with the 2 year old "handbook" basically stating they will "fall out" without notice and their new favorite words are "no" and "I don't wanna".
Here is what works with my son. If he starts to throw a tantrum, I either put him in time out or let him throw it on the floor but I always make sure to tell him to let me know when he's done so we can talk about it. and than about every minute or so after I walk away, I ask him if he's "done yet". Until he sort of calms down and than I sit him on my lap and ask him what's the problem? He'll tell me and than I'll either tell him why he can't do it, or explain to him that if he had calmly asked me say to play outside instead of throwing a fit, I would have gladly let him go, but instead he wasted time by throwing a fit about it.
He usually does okay with it. I try to get him to realize that talking about things and asking in a nice way usually works better than demanding or throwing fits when he can't have his way.
So far so good........good luck.
Oh and PS, it might get worse when the new baby gets here. I also have a 1 year old who is now walking and needs a little extra attention because he's determined to knock himself out on a wall corner........and the tantrums seem to have gotten a little worse since than. Just a forwarning.
I also know that when the tantrums become "regular" that he is feeling like he needs a little extra mommy time, so I try to get that in for him. Even if it means keeping him up a little later on a "school night" to play a game or read some books or just to cuddle.