Yes definately! I've had a couple of nasty bites on my past visits in early June. The last bite I did have though was about 6 years ago whilst on Nissi Beach during the day when obviously suncream was my priority not mossie repellant!
We don't bother with mossie sprays just make sure we start taking garlic tablets a couple of weeks before we go, seems to work.
We go in June and have already been taking them for a couple of weeks.
I get bitten alive when holidaying in Greece but have never had a problem in Cyprus, I still wear my Malibu aftersun with insect repellant just incase though as my mam gets bitten every year! Again not sure if it is something else as I have seen mozzies but never been bitten myself!