Actually no. You have to submit your unconfirmed transaction on the full hour but only when they are crowded with demands, usualy when the whole bitcoin network is working slow for some reason or there are some issues with transactions confirmation. In any other case you can submit transactions in any time of the day.
But even if you have to submit the transaction on the full hour that doesn't have to be exactly on a minute, you have about 5 minutes time to submit the transaction. For example if you try to upload on 20:00 p.m. your last attempt makes sense at 20:05. If you don't succeed then you can try again on 21:00 p.m. and have another 5 minutes to upload the transaction. Hope this is clear.