We've had our Cypriot ones for quite a while but never used them in Cyprus because we generally spent more than the amount you could use for contactless payments....
However, we do have them here in UK and as the cardholder - it's us who either put the card into the reader to make the payment personally, or tell the cashier you're using the contactless method and "we" wave the card over the reader.
You do have to be very close to the reader for the payment to be taken so don't have any worries that your card could be used if you're standing at another counter and be unaware of a payment being deducted for somebody else's purchases....
I would tell the cashier though, that you will wave the card - and not them!
If you have Cypriot bank text alerts set up on your mobile you will receive the text almost immediately the payment is confirmed by the reader. Our deductions were always notified to our phones in Cyprus before we had even put the card back in our purse or wallet