Custom reminder for call

I have created an ability on website for lead to choose the time of call.
I am setting several reminders in fixed periods before the call.
All this is through API v8 and that works fine.
Also I want to send an email with call details immediately after lead ends the setup process.
When setting reminders in field timer_email I set amount of seconds before the call when the reminder should be sent.
For example 5 minutes before the call, so I put here 300.
Following same logic I tried calculating how many seconds left to the call from current moment and set up additional reminder with this amount of seconds in timer_email.
From tests comes up that the reminders are not sent when the value of timer_email are not set as dropdown option for GUI.
In my situation this time can vary and I can’t set up hundreds of options in dropdown to make it work.

What are the options do I have to send an email with all details right after the call saved to system through API?