I use Browning cameras and an iPhone 7 Plus. The Apple SD card reader works great but if you have 10k+ pictures the iPhone (One camera this year had 27k due to misplaced east facing) you have two options. Import them which sucks the life out of your phone and takes over an hour when you have thousands of pictures, or let the iPhone read each picture (which takes quite a bit in itself) and all you get is a very small preview square which I would never recommend.
Two scenarios play out for my every year out west.
1. I'm always looking for new locations if I feel good about a spot I drop a camera and some salt in early July and come back by end of July to see what happened. I usually run this at smaller picture intervals. I'll show up to the site, grab the SD card, swap it with a new card, and will let the card extract to my phone. What I found last year was even with 1k pictures it still takes a lot of time. I ended up planning it so I could leapfrog to the next camera spot and not sit idle for an hour to see if the camera was worth keeping or take away. Depending on the extract I might go back and take the camera out (I'll take a new way back and keep scouting) or be stoked that I've got a good productive spot.
2. If I know the camera is in a good spot and I know I've got good pictures I'll just swap SD cards. From here I have two options, wait until I get home if I'm not hunting the area to pop it into my Mac or I'm currently hunting the area and it's 10am and I'm waiting to hunt elk in the afternoon I'll pop the SD card in and let it import as I hike.
Here are the keys to importing into your phone though while you hike! Turn your phone into lower power mode (Settings > Battery Low Power Mode) and keeping the phone in airplane mode (Settings > Airplane Mode). This little trick will save your battery while importing, it's nuts.
The caveat to those settings though is it KILLS your GPS accuracy. So, if you're using some like Gaia GPS just be aware of that if setting waypoints.
Yes, you can reformat the card on your phone (I think it actually just deletes) and pop it back in a Browning camera, how it works for other cameras I'm not sure.
Anyways, that's my two cents after playing around with an iPhone, the Apple SD card reader, and my cameras.