I have experience with several Tamron EF lenses + EOS RP, including Tamron EF 70-210mm f/4 and Tamron EF 100-400 f/4.5-6.3.
They usually work just fine (aperture, stabilization, focus) with latest firmware if Tamron says so. However, the AF scan speed is uselessly slow in situations where the lens+camera combination cannot find focus. In practice, this does not matter, as in 99% of the cases the focus will be found by jumping to the correct predicted position, not by scanning throughout the scan range. The jumping, in 99% of the cases, is extremely fast. The AF scan speed is slower the longer the lens is.
For what it's worth, the Tamron long lens AF scan speed is uselessly slow also in my cheap crop sensor Canon EOS 2000D camera. So it could be a property of the lens, not property of the lens+camera combination. (You can test this by zooming the 70-200 to its 200mm end, add a lens cap, and try to focus and see how quickly the focus distance scale moves.)
Also, some old firmware could have problems. Do buy a tap-in console and upgrade the firmware if it is compatible with tap-in console (the G1 lens may not be compatible). If it is still in warranty, you can also ship to Tamron service center if you do not have the latest firmware and are having compatibility issues. For example, my 100-400 with its old firmware had an issue where the AF scan functionality was not used at all. Firmware update fixed it (now the AF scan works, it's just slow).
Also, don't always believe Tamron when they say some lens works with some camera. For example, I once bought a used 24-70 f/2.8 G1. Its stabilizer did not work with EOS RP, but it worked with a cheap crop sensor DSLR. So it's a compatibility issue. Tamron said it should work without firmware update. I sent the used lens back to its seller with a note it doesn't work with R series cameras but works with DSLRs. A new 24-70 f/2.8 G2 works just fine.
You might want to use focus limiter and/or change the camera's AF settings to skip focusing if correct focus cannot be found. The latter can be found in the "custom functions" menu.
With EOS R5, it is not yet known if its in-body stabilizer works with third-party stabilized lenses and if so, how well it works. Apparently they are advertising it as "new approaches to in-body IS" so it can be digital (based on taking multiple images) instead of mechanical. They are also advertising it works together with stabilizer in RF lenses, leading us to believe it might not work together with third-party EF lens stabilization systems. However, in a press conference it was said that EF lenses work with the IBIS; not sure if this applies to 3rd party EF lenses.
My advice? Do either:
- Wait until we have reports of EOS R5 working with Tamron 70-200 f/2.8, don't rush to buy the EOS R5 immediately when available.
- Prepare to buy RF 70-200 f/2.8 if Tamron doesn't work with R5. It's not a bad investment; its weight and size are extraordinarily small.
Also, Tamron says this, apparently for your lens: