I'll comment on your last post first.
You're seeing a spike in military costs because you're charged for whatever military is funded, regardless of whether or not you use it. You're only charged for social when you use it, even when it's funded. The simple answer here is that since you're no longer building anything, the unused social is being transferred to military (with no bonuses, by the way), both decreasing your social expenses and increasing your military expenses.
The short version is that InfernalRS is (mostly) correct. The somewhat longer version is that the screens you're looking at aren't updating.
The part where InfernalRS is not correct is the part where he states that focused production is not subject to bonuses. It is-it is subject to any bonuses that happen after it gets there, but not before it leaves. (For instance, focusing production on research provides all base production that arrives at research with a research bonus, but it is irrelevant whether the base production is taken from social or military as neither of their bonuses are used.)
As InfernalRS has said, though, adding focus to the mix throws another wrench into the works, particularly as TA's focus mechanism is (intentionally) not as efficient as DL/DA's-that is, although 25% of the base value is taken from military and social and given to research, only 20% of the base value (or 80% of the value taken, if you prefer) is given to research.
Additionally, it seems you're playing on a difficulty higher than Tough and throwing off all of my numbers.
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However, it seems the real culprit at hand here is that the tech capital's bonus is stacking with the research bonus additively rather than multiplicatively (simplistically, it adds at most funding times base research, without accounting for any bonuses whatsoever).
This would seem to most definitely be a bug, as it works properly (multiplicatively, i.e. doubling the entire planetary output) in DL/DA. Looking at the XML I can't see a difference, so something must have changed in the hard code. 
It's also a possibility that both your game and my game are bugged, though, so I'll wait on someone else for confirmation. (Rather simple: Load up a game with a research bonus, cheat/research your way to tech capital, add money to "account", rush buy tech capital, compare before and after numbers.)
Random talking to myself (otherwise known as numbers) is shown below.
It's duplication time.
I have no bonuses on my randomly generated homeworld, so we're going to fake it.
Xeno lab on a 700% tile = 8 xeno labs, +1 xeno lab, + innovation complex, + manufacturing capital, + tech capital, + starport, + civ capital = 14 buildings. Good thing I've got space.
40% research bonus from political party + customization points, 10% from planetary improvements = 50%.
10% social from industrial revolution, 10% social & 10% military from planetary improvements, 33% bonus to industry on homeworld from manufacturing capital, 10% bonus to industry from moon.
23% military funding, 27% social funding, 50% research funding, 100% overall production slider funding.
79 research (101 tp as displayed in improvement summary screen from colony management screen), for which I am being charged 50BC (domestic stats, economy, research) in addition to 16BC under bonus production/research (the two are unfortunately not distinguished from each other in that screen). This is before adding the tech capital.
If I switch focus from off to research, I now have 82 tp shown in the colony management screen, and am being charged for 52 + 16 bonus.
After building the tech capital, my numbers are 130 tp in colony management (101 tp in improvement summary), 135 tp with focus on research, and 50 research spending/40 bonus production spending without focus as opposed to 52 research spending/41 bonus production spending with focus.
For what it's worth, my above numbers don't take into account your building the tech capital over the non-boosted xeno lab, so they're off of yours slightly. However, we can also see that even my base number of 79/82 is lower than yours of 91. I assume you're playing on a difficulty higher than Tough? A hidden research bonus is given to the player when a research bonus is present, of sufficient magnitude that it outclasses the research bonus itself at Suicidal, so I'd wager you're playing either Painful or Crippling from the looks of the bonus. Either that, or there's something we're missing.
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My research screen shows the number of BCs that I am spending on research, but not on bonus research. In addition, it does not update until you fiddle with the sliders-or end your turn-and neither does the economic policy screen.
The best solution is simply to go out and "hit" your research up one point in the economic policy screen, which it won't actually go up any (still at 50%, not 51%), assuming you've taken it all the way to the right before modifying the other two to give yourself a 50% research output.
Important notice about bonuses (military/social/research): Half of the bonus you pay for, and it shows up under "bonus production/research". The other half is free, and therefore does not show up anywhere but in the planetary screen.
