I have an outpost with 120 max shield (20 shield + queen + 4 kings). My tinkerer is there as well, and the outpost currently has 11 shield. When I scroll forward in time, I find that the outpost stays on 11 shield, that is, the outpost recharge is entirely cancelling out the -3 shield charge by the tinkerer, however if you do some calculations:

+120 shield in 48 hours = +120 shield per 2 days
-3 shield every hour = -144 shield per 2 days
Therefore the net charge is -24

However the shield charge is just staying at 11 and not moving at all, and whats more, if I move one or more of my kings from that outpost, the shield starts decreasing again...

My initial thoughts are that the tinkerer actually has a -120 shield charge per 48 hours its just that when you round it you get -2.5 per hour which rounds to -3, but maybe the Devs didn't want to put a -2.5 because it looked bad?
Anyone else experienced this?

This would also answer the question about how much shield charge you really need if you wanted to have a tinkerer without any net loss of shield...

Could be that the Tinkerer mod is precise, at -3. However the +120 may not be precise, because thats a number built from lots of different sources calculated by many many ticks in increments of time.

It must be a rounding issue.

The tinkerer causes your shield to drop by 1 every 2nd 'tick'. Your shield is gaining 1 shield every 2.4 'ticks'. If the game is rounding this then that would result in no net gain/loss.

Not ideal, but sometimes it's easier to live with minor 'errors' instead of having to restructure the entire code to fix the issue.

That's my guess anyway.