it does not provide specialization, however if you had the versatile specialization feat I would rule that it gives you the desired effect.
Based on e rules text quoted above, if a class ability from the class granting specialization grants proficiency, then you get specialization as well.
Other sources of proficiency, such as feats, spells, or other class levels with less than three levels, don't also grant specialization unless specifically stated.
I'd agree with others that you do not gain Weapon Spec automatically with Technomantic Proficiency. The 3rd-level class ability grants bonus feats, you are only gaining proficiency temporarily and only for 1 weapon, and in any case there's no such feat as "Weapon Specialization: Hunting Rifle", for example.
This does make Technomantic Proficiency rather crappy. I think it would be pretty crappy even if it did grant WS, except maybe at high levels. So if I were the DM I'd go ahead and let Weapon Spec apply (assuming the adventure starts at Level 1), since I'm pretty tolerant of bending rules for underpowered builds.
RE: Versatile Spec + Technomantic Proficiency, that's sort of a complicated question.
Versatile Spec indicates that it grants spec to weapons that can be "selected with Weapon Specialization".
The pre-req for Weapon Spec is proficiency. So can you select a feat whose pre-reqs you only meet for minutes at a time when using a special ability? You're not technically doing that here, but that's the requirement to see if Versatile Spec applies to the weapon.
AFAIK this was only loosely resolved even in PF.
Here's the dev response for PF:
http://paizo.com/threads/rzs2l4kc&page=2?Feats-Prerequisite#91
SKR's response there suggests allowing it if it's a 24-hour sort of bonus but not a short duration bonus like this. And obviously SF is not PF, but the language regarding feat pre-reqs is identical between PF and SF.
So my strictest reading of RAW, using the information available, is don't have Versatile Spec apply (and therefore it's impossible to get Specialization with Technomantic Proficiency). Which is probably the ruling I'd enforce for SFS, unless a SF dev says otherwise.
This is an example of something granting both proficiency and specialization.
Combat Tracking (Ex) 1st Level
Your exocortex provides you with enhanced combat ability, granting you proficiency with heavy armor and longarms. At 3rd level, you gain weapon specialization in longarms just as if your class granted proficiency. As a move action during combat, you can designate a foe for your exocortex to track. As long as that target is in sight, the exocortex feeds you telemetry, vulnerabilities, and combat tactics, allowing you to make attacks against that target as if your base attack bonus from your mechanic levels were equal to your mechanic level. Designating another target causes you to immediately lose this bonus against the previous target.
Side note: Strange how the code messed up. Typing on my phone so whateves.