No, you have nothing to worry about.
Once seeds are planted, you don't need to do anything with them until the time is up. When the required waiting time has passed, a green "harvest" button will appear on the meadow(s) which allows you to collect the produce. You will also receive a notification when the crops are ready to be collected, on the 'bell' icon next to your message inbox in the top-right corner of the page.

There is also no time limit to collect the harvest once it is complete - the green 'harvest' button will remain until it is clicked, therefore you don't need to worry about losing your crop harvest either.

Thank you for answering and for the extra information! Just wanted to be extra careful since it's pass seeds and I didn't want any to go to waste!