Cambridge English Dictionary lists three pronunciation for 'is':
strong /ɪz/ weak /z/ /s/
The usual pronunciation of 'is' is /ɪz/, but as your dictionary says, it can assimilate to [ɪs] before an unvoiced sound. There's a tendency to make nearby sounds more similar to each other, so when 'is' is followed by another word beginning with an unvoiced sound, the voicing of 'is' is turned off and it becomes [ɪs]. Note that the only difference between [ɪs] and [ɪz] is voicing.
Before /ʃ/, 'is' is likely to assimilate to /ʃ/ as in it is shining. Before another /s/, it often geminates (lengthened): ... is sunny.
Before /z/, 'is' is likely to become a geminated z: ... is zoo.
So yeah, your dictionary is basically right. But don't expect everyone to assimilate their 'is's.