I believe you, however I have worked with many star/delta, auto transformer, and resistor starters and never found that problem. However I have had some odd faults which did not seem to make sense. One case was a crushing plant used once every blue moon to crush rock to repair a road. The motor was tripping out, but tests on the motor showed no fault. However my test gear could not detect something like a short between wires in the same winding so there was a slight chance the motor was at fault, what I wanted was a way to measure the torque.
The mechanical engineer arrived on site and asked what the problem was, it was explained, and much to the dismay of the fitter he directed that the bearing cover should be removed and two hands full of grease removed and re-try and see if any better. Both myself and the fitter thought this was a waste of time, but he was the boss, so block and tattle was rigged the cover lifted and two hands full of grease removed. One getting everything bolted back down and re-trying it actually worked.
When the mechanical engineer returned we asked how he knew it was the problem, answer I have had it before with infrequent used machines, the operator always greases when he has finished but it does not run long enough to dispel that grease.
In your case with fans the load is unusual fans being free to run but air pressure likely to build up similar to how I found it with the water pumps, a quick change over happens before there is a back pressure, a slow change over and a back pressure has built up.
With large pumps we did not use star/delta, mainly resistor start was used, often 5 stages. So there were 4 large resistors, on each winding, on start all four are in circuit and then four contractors one by one short out the resistors, this means at no time is power removed, so back pressure can't cause the motor speed to suddenly change, I had never really thought about this being a reason for resistor start, to me it was just a more gentle start to star/delta but we often had to change resistors with crushing plants where it had stopped full and the operator had tried to restart it without empting it first.
Today electronic drives have replaced most of the star/delta starters and they are becoming museum pieces. Specially those with dash pot overloads.