Tripping of the little red button had nothing to do with the amount of hot water you used. If both elements are working then the only place the tank can be at a lower temperature than ambient is below the lower element. In turn condensation could only occur below the bottom element. If you have water in the thermostat area you either have a tank leak or a fitting leak (above the noticed water).
The red button trips due to either a stuck thermostat or an element with a crack in the sheath, usually the latter. Thermostats only open one leg of power to the element. If a element sheath crack develops, the hot leg continues to supply power to the element. Circuit continuity is made through the crack and water to ground. Heating is usually slow so most red button trips occur after long periods of no hot water usage (i.e., early morning hours (0500)).
If your tank is many years old and you have not changed the anode as recommended on this site, you are probably looking at a new WH.
Thermostats are designed to respond to tank temperature. With the tstat cover off the tstat will be affected by air temperature and the WH will have to get to a higher temperature before switching. You lose some margin of safety in this mode.