Colors printer for sublimation look dull

What is your printing workflow? The chosen settings, such as working with ICC profiles, are key to quality and repeatable prints. Perhaps, you can share screen captures of your print settings for review.

warmly/j

Ideally, you're going to need to use "Photoshop Manages Color" and select an ICC profile made for your ink and printer - plus the media. Also, the 'media' selected by name in "Print Settings" should be correct for the supplied ICC profile.

You'll also have to treat any heated pressing process carefully to maintain consistency (IF that’s involved here). 

Inks and media have a maximum gamut. That colour range is the best it can do. Have you seen good results from this manufacturer's materials?

Start with an RGB image in the Adobe RGB colourspace and test that, please go here and download the Adobe RGB testimage: https://www.colourmanagement.net/index.php/downloads_listing/

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

You should always test output using good color reference images designed for that task. The color reference images RGB values are such that they are set for output and are editing and display agnostic. Test the output this way and examine for the same color issues so we know it's not your image-specific issues causing the problems:
http://www.digitaldog.net/files/2014PrinterTestFileFlat.tif.zip

@Brand-It 

Was the file CMYK mode? It should be RGB...

Third-party ink and third-party paper! OEM printer driver settings are often based around the OEM ink and paper, if you use others then you need a lot of trial and error to get the best results. Also consider some light/medium/dark neutral grays in your test file.