Does it take you a great deal of practice, or does it come naturally to you?
We've had some cold mornings and warm afternoons. So we could be talking about a significant difference in ambient temperature, plus the the addition of heat generated from friction. As we are talking about a tandem, we have larger forces at play acting on the tyre and potentially higher speeds.
The maximum recommended tyre pressures printed on the side of the tyre are the inflation pressures that assume normal use. I would expect there's plenty of safety margin manufactured into the tyre - but my experiences of riding around on a fully loaded tandem and being able to maintain 30 mph for long stints on flat or being able to accelerate quickly up a climb in order to go from being on the tail end of large group to the front of a large group on club rides suggest to me it is a possible corner case, if the tyre was inflated to the max indicated pressure on a cold day. Especially given that the rim width/tyre/width/nominal pressure/load have not yet been disclosed.
The amount of friction generated by properly inflated bicycle tyres is so small that it cannot even raise the temperature of the tyre. You can raise the temperature of a tyre by pedalling on one of those trainers with a very small roller and a soft tyre. That generates a reasonable amount of heat - say an increase in 20 or 30 degrees. But, you'll know if you have done it, it destroyes the tyre (from unnatural flexion, not overheating) and, it is very, very hard work. Further, a bike that travels real distance has cooling air circulating around the tyre whereas a static bike doesn't.
Therefore it is safe to assume that tyre friction on a loaded tandem is not going to heat up the tyre.
Now lets have a look at what artificially heating a tyre does to pressure. Since tyre diameter does not change with inflation, the volume of a hot or cold tyre is constant and we can use Gay-Liussac's law to calculate the rise in pressure with the rise in temperature. It turns out that if you heat a wheel with tyre inflated at 100PSI from 0 Degrees C to 100 degrees C the pressure goes up by 34PSI. I.e. you end up with 134 PSI.
Let's talk about cold mornings and warm afternoons, let's say 0 degrees start and 20 degrees warmer later on.
Then your 100PSI tyre would go up to 107 PSI.
It is plausible that if your tyre is rated at 100PSI Max and you heat it by 100 degrees, you'll have a blow-out. But is this a realistic scenario? No.
It is not plausible that a good tyre rated at 100PSI will blow off at 107 PSI.
One calculation kills a lot of speculation.