it is very nice of you to post your experience here in order to help others.
Let me take a moment to help you understand better what happened.
First, the tls module amsn downloaded was compiled against libssl0.9.7 which was the latest release at that time if I remember correctly. You didn't have that lib on your PC which is why it didn't work (that's always the problem with linux, everyone has a different version of everything, so most linux users have to compile everything on their own).
I think you could have simply done 'apt-get install tcltls' and it should have work (it's written in the wiki).
Secondly, you say amsn doesn't care about the folder you specified for TLS. That's wrong, it's actualy how Tcl works, what we do with that directory is that we simply add it to the 'auto_path' variable of Tcl, which is a variable telling Tcl which directories to search when a 'package require' is specified (at that point, it looks in each directory for the pkgIndex.tcl file which states 'package ifneeded tls 1.5 "load libtls.so"' ). Now, you specified a directory, so that directory was added, but as any directory is added in a 'path' variable, the first paths are searched first.. if you deleted the tls directory from your plugins directory, it would have not found it there and would have searched in the next directory, which is the one is specified and it would have loaded the TLS package you compiled (which would have worked since you compiled it yourself).
Unfortunately, with Tcl we can't say 'search for a package in this directory', in the same way you can't say in Bash, to launch a command from a directory (unless you specify the whole path, but then you launch an executable, not a 'command'), so it always has to depend on that path variable.
Sorry you wasted 4 hours of your time over this, I'm sure you could have found the answer by either asking in the forums earlier, or asking on the IRC channel if someone was available to help you.
Nonetheless, I congratulate you for your perseverance and for you being able to find the solution on your own. It means you're good at figuring out things on your own, which is the basic skill needed for becoming a geek
(unless you already are
Thanks again, and I hope this answers your doubts.