Using the same picture on Moab mat paper and luster I'am out with a different look. On mat it's as on screen, while using luster the image as a perceptible red tone throughout. I am using the latest Mac on Photoshop with a Canon pro-100 printer, with the exact profile for both paper.
Strange.

If you soft-proof the file in Photoshop before print, do you see the red shift on-screen? If not, then there is likely a print setting issue to blame.
Are you using our recommended media settings for both papers?

Using soft-proofing there's no red shift on screen and I am using the right color profile for both paper.

Today I made 10 tests with the same picture on different 8 1/2 X 11 papers.

1- Costco's gloss with printer management without Moab profiles: Good greys and colors, winter scene.
2- Costco's gloss with lasal luster profiles: good.
3- Moab Entrada natural, entrada profile: pink
4- Moab Entrada with printer settings: pink
5- Staples matte with Entrada profiles: pink
6- Staples matte with Moab lasal mat: good
7- Staples matte with Moab lasal luster: good ???
8- Moab lasal luster with lasal luster profile: pink
9- Moab lasal luster with Lasal MATTE: good, the closest to screen
10- Moab lasal luster with Lasal luster setting using platinum on PSCC: pink

So printing on lasal luster using lasal matte profiles seems to be a strange, but good solution.