The TSS request is entirely server-side. Nothing further will happen on your phone. Saurik's server now has your phone's ECID (which it had already...it's how Cydia tells your phone apart from anyone else's). He has no other personal information. As soon as it makes sense to have it on file, Saurik will have the server request signature info for 3.1.3, and then the message will change from TSS pending to "This device has SHSHs on file..."
There is absolutely no reason at all in this or any other world why you would not want your signature information on file with Saurik. It could someday save your jailbreak/unlock, and there is just no downside.
Finally, signature requests contain no personal information. And even if they did, I would trust Saurik with my information before I'd trust Apple. Besides, if Saurik wanted to steal your personal info, he wouldn't be telling you about it and asking your permission!