They don't only appear to you.
When planes get added, they get added in groups of 50.
If you call the market and see '0 planes have been added since last call', then there have been no groups added.
If you call the market and see '47 planes have been added since last call', then a group of 50 has been added, but 3 planes have already been grabbed by people who called after the update, but before your call. If the plane you attempt to lease is being leased by someone else, that's because they called before you did as well. Look at the time remaining, where it says 'someone else is trying to lease this plane, try again in 1.8 minutes'. That timer lasts for 3 minutes, so if there's 1.8 minutes left, that person clicked 'lease plane' 1.2 minutes ago.
apart from there being a lot of demand for used planes, and a lot of people calling and grabbing what they can, there's another reason you'll have to be lucky. People pool their calls, allowing a lot more regular checks to be made. Instead of a call every 35 minutes the way you have, a group of 10 people can make a call every 3.5 minutes if they want to, so they'll almost always see a new group of 50 within 5 minutes of it appearing, and can report on what's there. Then all the other members can call as well to have access to those planes. Plus, people will hold planes for their friends, by clicking 'lease plane' on a plane they don't want, which holds it for 3 minutes. It's possible to end the hold when you want to, and time it with someone else starting their hold, so you'll never get a chance to lease it, unless you're lucky enough that your call is after an update, but before any of their calls.