I get a notification automatically on my phone when a new episode is available (I don't know if it's Google Play Music or Google Podcasts that notifies me, but it's one of those). That triggers me to bring up the podcast in the car. I guess if you listen to a lot of podcasts this method isn't all that useful (I only listen to two, so it's not too bad).
But yes, support for podcasts in TunedIn is pretty horrible. First of all it doesn't appear to support episodes over an hour at all. Maybe if you are lucky you can get it to start, but the time is wrong and sometimes after it gets past a certain point it just stops.
More important, if you change audio sources at all, or if there is some kind of glitch, it completely forgets where you were, so you need to fiddle with it and hope you can get somewhere close to where you left off.
I've basically just given up on the one podcast that is routinely over an hour episode length and just stream that from my phone over Bluetooth, but like your comment on Spotify, it just seems so unnecessary.