It is more important to be understood than to abide by the finer points of pronunciation.
In classical Greek our plant was named by, for example, Dioscorides, as 'clematitis' (connected to clematis) or 'clematides' (resembling clematis). 'Clematis' was reserved for periwinkle (Vinca). Dioscorides also used the term Clematis altera for the clematis that were not periwinkles (altera - 'the other'). Clematis viticella was known to the Greeks and the Romans being native to their countries. The four blue tepals of the viticella would invite comparison with periwinkle. At some point in the late medieval period the name left the periwinkle and firmly stood for our climber.
As all the authorities are agreed, there is no difficulty with this name. We can consider it under three syllables:
Cle has a short 'e' and the syllable is pronounced KLE as in 'cleric'
ma- 'a' is short as in apart
'tis 'i' is short and 'tis' rhymes with 'hiss'
For clematis we have: kle ma tis
Plural is clematises but its awkwardness has led to its being discarded. Therefore 'clematis' is used for one or more than one plant.
See: Howells, J. 1999. Trouble Free Clematis: The Viticellas. P.31.