It's likely that eventually the bar will lower and people will stop minding less integrated ads. But the advertiser pays per download (right now, see next paragraph) and doesn't pay the host to do the reading, so from the buying end it's simple and generally they work with the Podcast hosting platform who then farms it out to creators.
NPR released their Remote Audio Data spec recently and many players are working to integrate it. Essentially the ID3 tags have several time stamps marked and a call back URL. The podcast player then delivers events to that URI indicating the listener listened through that time stamp with some other metadata.
The automation and ad network-ization is already in motion.
So to answer: the same place web pages get ads.
Do you have any information on who? I've mostly heard about players announcing they won't support it, and Apple and Spotify have their own analytics systems they'd probably prefer people use.
The big thing is Apple. Apple is definitely the big boy in the pond and NPR is in talks to get it working.
The thing is, if other podcatchers continue to refuse to provide data somehow, the advertisers are going to start refusing to pay for downloads and only for impressions verifiable on Apple, Spotify, and Google's apps. The end result is the closing off into walled gardens.
We already have Stitcher and Spotify buying up podcasts and keeping them exclusive to their platforms.
It can go either way but like...it's bad if it doesn't go this way. Either you're buying podcasts per episode or trapped on Google/Apple/Spotify's horrific podcast apps.
The apps are horrific. Google compresses audio to the point you get obvious quality loss and artifacting, even to my non-audiophile ears on $20 earbuds.
Apple Podcasts is a PITA once you've subscribed to more than 10 podcasts. It's really badly set up if you subscribe to a serial audio drama and have several seasons to catch up on.
Spotify thinks podcasts are just playlists in order from newest to oldest and wow is that a barebones and impossible UX for anything but a talkshow type podcast.
EDIT: Forgot to mention, all that to say, it'll probably come from markets that fit how/when/where consumers listen: exercise, entertainment, etc.
