Trains are mass transit in Switzelrand, just like in Australia. The SBB network is the same size as the Sydney Trains network. And it operates on a “turn up and go” basis, just like in Australia.
So to get from Interlaken you buy a ticket from Interlaken to Bern, and what you get is just a time and zone based ticket for the Libero tariff system. So you have unlimited travel on all public transit in the zones mentioned for 180 minutes after the time mentioned on your ticket.
You can see the zone map here:
https://www.mylibero.ch/sites/default/files/2025-12/Libero-Gesamtzonenplan-2026.pdf
Public transit works like that in many places in Europe. You have a zone system, and to travel you buy a number of zones, and can use any public transit within those zones.
If you have two tickets one with validity starting at 9:59 and another starting at 11:59 you did do something odd there.
Are you only going one way, or are you doing a day trip? Because in that case buying a day ticket (which is twice the price of a single) is that best option, as that gives you a whole day of unlimited travel in those zones.
Also there is absolutely no advantage, and quite a few disadvantages in buying such tickets in advance. This is mass transit. You can easily buy these tickets on the day itself. When I go to Bern I usually buy the ticket richt after I have put my hat on to get out of the door :-)
Maybe just see if you can cancel the tickets. Your plans might change.