Snapedom

No, neither of his masters tongue-ties him because each of them wants to know what the other is thinking so they feed one another selected true information.

Originally I thought that that was a reading that worked logically, but then I thought about it more and found that it wasn't quite working for me. That explanation only works if you have both masters SIMULTANEOUSLY accepting him as a double-agent from the get-go - because otherwise the one master would have no reason to believe that the other had NOT put the curse on him. And that (at least to me) is not clear in canon, due to JKR's vagueness.

If, for example, Voldie sent him in with the intention of having him spy, but without the idea that he would pretend to be Dumbles' agent (as seems likely from his ordering Severus into the DADA post - you can't tell me he didn't expect useful info from that as well as the fulfillment of another, 1-year mission) he would likely have put the curse on Sev to prevent him (purposefully or accidentally) sharing anything of importance. And also, why would he have serious reason to expect that Dumbles would not put the curse on any new hire coming in with a past as shady as Severus,' just as a precaution? (Dumbles might not DO it, but why would Voldie not EXPECT him to do it?)

That is, the lack of the Tongue-Tying curse on Sev works ONCE you as the reader are ALREADY in that situation with him; it's the getting there without it that I find problematic. (Hope that makes sense?)