The air put in the tyre will be significantly warmer than ambient temperature whilst pumping up, amount depends on the pump used and the effort put in to some extent - unless using a CO2 inflater, that tends to be cooler.
The effect is more significant with a total inflation than a top up. The temperature of the pump should give a clue as to how much by, larger/heavier pumps are affected less.
CO2 is also slightly soluble in butyl, so that component of the air in the tyre will reduce over time as the CO2 migrates to the lower pressure.
Also water content of air is prone to a massive volume change when it transitions from warm vapour to cooler liquid.
The science is complex - most demonstrations/experiments go to great lengths to minimise/eliminate one or more of the variables.
In the real world you need to guess how much extra (or less) to put in the tyres to compensate for the method of inflation and the expected changes of environment.