Ask yourself..."Is this job better then the one I'm currently at and will I gain more experience from it?" Yes, you definately will at TSA, but from what I've seen ASA is a lot better company. I am very suprised they are even having classes in January. We are still extrememly fat on reserve pilots and I would not be suprised if they cancelled the class and offered you a job at HoeJets (Thats what they've done to the past couple of classes).
I know how hard it is to stay as a CFI when you possibly have your first real job out there. But, I do have to say this...when ASA calls, get the hell out of TSA. The contract is coming up this summer and the pilot group is going to get screwed over big time with HoeJets.
I wouldn't base your decision either on which company has the fastest upgrade time. How can you tell what is going to happen 2,3,4 years from now, let alone one year? Go to a place where you think you will be the happiest and let the cards fall into place.