Thanks for your question - I am Sam and I am one of the UK tax experts here on Just Answer.
Yes your understanding is correct as these payments were made due to connection of their employment (or cessation)
The fact these came from your personal account and that you wish to treat them as gifts I am afraid, cannot be so.
Ideally you would have taxed these gifts (and subjected them to national Insurance) prior to payment but as this was not the case I would advise
1) you write to each of the employees detailing what should have taken place for them to declare this payment to HMRC and
2) You alert HMRC of the same so you can pay and Class 1 National Insurance (employers) and consider whether you also pay the tax that should have been deducted along with the employee National Insurance.
Please advsie if I can assist further
I can send an additional service for me to telephone me if you would prefer (I am in the UK) - this will incur an additional fee or I can respond here - but the answer I gave remains the same (only the failure to pay then sits with just you)
You are welcome and thanks for rating the service, much appreciated