Just happened to me that I inflated my car tyres in an usual petrol station. Surprisingly, finished inflate each tyre I noticed that there are some water spraying out from the nozzle. Further checked found that there might be some water in the compressor due to the air was compressed. Compressed humid air (humidity) = water.

So my question being, little bit of moisture/ water in the tyres, will cause some side effects to the tyres?

I also believe it is no big deal.
First the problem is, what are these water going to cause?
Most of the rims nowadays are made by alloys and corrosion resistance, meaning excess water won't cause much problems to the rims, unless it is an old steel rim.