You're right in that systems like EVDO can't be used with UMTS, but you're introducing inaccuracies in the way you argue it. UMTS runs over a variety of air interfaces, none of which are TDMA.
W-CDMA is a CDMA air interface, like IS-95 (which is the air interface specification that's frequently referred to by the name "CDMA", but this is misleading as the words refer to a type of multiplexing, not a specification and protocol. IS-95 is a specification and protocol. Likewise IS-136, also known as D-AMPS, was frequently called "TDMA" in the US, but both GSM and IS-136 use TDMA air interfaces, using completely different implementations. GSM's is actually wideband and frequency hopping, making it a spread spectrum TDMA system.)
UMTS runs over W-CDMA.
A modification to W-CDMA is HSDPA. This is still a CDMA air interface (it's only a modified W-CDMA.) UMTS runs over HSDPA too, and indeed that's the air interface used for UMTS by Cingular.
Yet another modification to W-CDMA is HSUPA. This is also still CDMA, and UMTS runs over that.
While I'm just throwing facts out there, UMTS can also run over 802.11, using a system called UMA. (GSM can do the same thing)
Anyway, nothing about UMTS is TDMA. It's using CDMA (except for 802.11 which is an essay by itself.) It's not the same CDMA specification and protocol as Sprint/Verizon, but it does use a CDMA-based air interface.
What are the differences? Well, the big one is that Sprint/Verizon's CDMA, which is known as IS-95 and IS-2000, and/or cmdaOne and CDMA2000, use 1.5MHz slices of spectrum, whereas W-CDMA uses 5MHz slices of spectrum. This, and other protocol and encoding changes, means W-CDMA is better at handling a variety of different types of data (in terms of the reserved bandwidth you need for audio/video, and more bursty pattern you need for web access, etc), though supposedly it degrades poorly as you go further from a tower.
For more information, take a look at
Wikipedia.