Abbreviation: Di-II = "Digitally Integrated (APS-C)" (Tamron)

The abbreviations means "Digitally Integrated (APS-C)"

Explanation from Tamron

Digitally Integrated Lenses Optimized for APS-C Format Digital SLR Cameras
Tamron Di-II lenses are engineered expressly for digital SLR cameras with image sensors commonly referred to as APS-C, measuring approximately 24mm x 16mm. Rendering an ideal image circle for APS-C sensors, Di-II lenses also include properties to optimize digital imaging performance.

See examples of effected products

Tamron SP AF 17-50mm f/2,8 XR Di-II LD Asph IF
Tamron SP 11-18mm f/4,5-5,6 Di-II
Tamron AF 18-250mm f/3,5-6,3 XR Di II

See links

tamron-usa.com