Not an expert, but you are correct the more your coolers run the greater chance you will experience condensation which increases the humidity. The longer the TE coolers run, the greater the chance the aluminum on the interior heat sink will drop below the dew point and start affecting the humidity. You counter this by quickly cooling down your humidor. TE cooler(s) will only reduce temperatures gradually, much slower than a compressor, so your cooler is constantly running. If your cabinet only has one TE cooler then it's probably working overtime trying to cool the humidor. If your humidor configuration allows, you can always try and add additional TE coolers in order to shorten the run time when cooling the humidor.
As temperature decreases in the humidor the humidity is most likely to increase and if I'm reading correctly, you are trying to keep your humidor at 15 degree C. If so, that's a tall task to ask one (if that's what you have) TE cooler to try and maintain. You may want to consider raising the temperature in your humidor. Another option is to decrease the ambient temperature in the room where the humidor resides.
I am currently in a situation where I have out grown the storage in my current climate controlled humidor (Remington) and recently placed an order for a large Avallo temperature controlled humidor. My current humidor has a compressor and when it kicks on it cools rapidly and in the process it removes humidity at the same time, but humidity recovery is always quick. In the Avallo humidor I added four (Quad) TE coolers to try and reduce the time it takes to cool the humidor to my desired temperature, therefore reducing chances of excess condensation. I also plan to maintain the humidor at 66-67 RH and 68-69 degrees too. This climate is where I believe optimizes the condition of my cigars best and hopefully will keep the humidity spikes in check. Good Luck!