There may be some possible, residual side effects, after you get a deep tissue massage. You're accessing the tissue pretty deeply, and you're going into muscles that sometimes haven't been touched in a long time, if ever. You may feel the next day, as if you've worked yourself out. You might feel a little bit sore that way, and that is normal and natural, and in those areas where you feel that way, it's probably a good idea just to add a little bit of ice, for under 10 minutes.
Maybe stay away from heat at first. I know we all love the heat, but ice is something that'll be better for you. Just in case, if there is a little bit of inflammation in the body, you're going to want to stay away from heat, because that will exacerbate that. But a little bit of ice can't hurt anything. Typically, you might feel just again a little bit sore, but you'll begin feeling so much better than you did before you got the massage within a couple of days, you'll quickly forget that that pain was there at all.