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

The abbreviation Di-II means "Digitally Integrated (APS-C)" and is seen on Tamron products.

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 F2.8 XR Di-II LD Asph IF
Tamron SP 11-18mm F4.5-5.6 Di-II
Tamron 18-250mm F3.5-6.3 XR Di II

See links

tamron-usa.com