People say that the pin must be pressed down in order for the air to get in. But when I try to remove the pump head by unlocking the lever, too much air leaks before I get to remove the pump.
I do two things - I overinflate the tyre by about one stroke of the track pump, and if the pump has a lever I flick it off pretty smartly. However my pump at home is a thread-on track pump and doesn't have any issues with pressure loss when slowly unscrewing the hose from the valve.
Also, try another pump. Borrow one from another cyclist, or check the LBS for an air line. Some bike fixup workstations have a pump built in too. Last resort is to try a car air pump at the local service station, though they can be quite brutal.
If you use a track pump, leave the handle in the up position while disconnecting the hose head from the valve, and you'll see the handle fall under its own weight. I bet the HISSSS of air moving stops at the same time the handle bottoms out, suggesting that the released air is coming from the pump not the tyre.
Lastly for self-reassurance, check your tyre pressure by hand before removing the pump hose, and again immediately after. You'll have a good-enough muscle memory for the pressure needed by your thumb to dent the tyre's tread. I expect it to have exactly the same perception of resistance to your thumb before and after hose disconnect.
Minor clarification - the pin does NOT need to be pressed down in a schrader valve to add air. If the air in the hose is high-enough pressure to overcome the internal tyre pressure plus the spring pressure, then air will go into the tube (barring no leaks or sticky valves)
There are different kinds of pumps. The usual pumps can indeed release too much air for certain purposes - mainly for high pressure low volume applications. That is the case for fork shocks and small wheels like my 8inch 7.5bar Skike wheels.
The solution is to use a . Those are designed for these applications, are detached quickly by unscrewing the inflator and release very little air in the process. It is also possible to put most off the air quickly by an ordinary high-volume pump and finish it off exactly with a shock pump. Some shock pumps also feature a high volume/high pressure switch.
However, I do also often just pump the Skike tyre with a cheep track pump. It can loose around 0.5 bar (remember - low volume!) but one can learn to disconnect the inflator quickly enough. Open the lever that holds it in place and then get the inflator from the valve as quickly and as directly as possible. You do lose some air, but it can be mitigated and you can also fill a bit more than you need if the amount becomes predictable.