Yes, most podcasts are hosted outside of your podcast player and distributed via RSS (even if this is Spotify which already hosts music).
So when a service has the podcast it means it lists the response from the RSS feed, but usually they just copy the text data, including the URL where the actual audio is stored.
This audio is served by whatever other service the creator of the podcast uses, which means you’re a free user to that service even if you pay for Spotify, which means the wonderful benefit of ads.
And these are ads you can’t block since they’re included in the audio stream (yay! /s).
Podverse (the player I use) mentions this as an issue when creating clips of the podcasts because they can’t know how much the timestamp has been offset by those ads, so your clip probably only sounds good to you.
IIRC they mentioned is next to impossible without actually processing the video and guessing when then ad stops on your client (since the ads will change per user, so it can’t be done on a server for all users)