I can confirm having the same issue: printing a TIFF vs placing it in an Ai file can get different RIP results in the same color space using the same rendering intent. TIFF color profiles seem to be ignored sometimes by the RIP in both Onyx and Flexi.
I actually tested this a couple of weeks ago in Flexi Production Manager, trying to finagle the most dependable print workflows.
I tested RIPs with four sets of four files, using one color space profile per set:
1) a TIFF file (saved from Photoshop with "Color: ICC color profile: ____" checked)
2) a TIFF placed in an .ai file with the same working color space, saved with the "Embed ICC profiles" button checked
3) a PDF file with Color Conversion set to "No Conversion" and Profile Inclusion Policy set to "Include All Profiles" set in the save settings
4) a PDF saved with "Convert to Destination" with the destination color space matched to the placed TIFF, with "Include Destination Profiles" set
I tested sRGB IEC61966-2.1, Wide Gamut RGB, GRACoL, and Printwide input profiles. The Ai and PDF files ripped similarly, but the RIP seemed to ignore the TIFF's embedded profile. The RIP result had typical signs of color space mismatch: having the saturation dramatically blown out, or colors muddied and hue shifted red->orange/brown or blue->purple/cyan. The former is usually what happens if a bigger gamut is displayed or linearized with a default/smaller color space, and the latter is due to a CMYK "crush-down" because the RIP thinks all the colors are way out of gamut.
What's really a puzzler is that the TIFFs still ripped wrong after I turned off "Use embedded ICC profiles" in the RIP, then manually set the input profile myself. Haven't tried that with Onyx, as we're not running it anymore.
Personally, I've found using PDFs as a "container file" gets the most consistent Onyx results, while Flexi seems to digest .ai files best. And sometimes, if a customer's raster file is fiddly when I try to place it, sometimes opening it in Photoshop, saving it as a .psd, then placing that instead fixes things due to Creative Cloud voodoo.
Mileage may vary based on your calibration, setup and printer's ability to remain in profile, but I hope this helps.