I believe that all verbs that end in -ide (/aɪd/) regularly produce adjectives ending in -isive (/aɪsɪv/) where the diphthong is preserved.
In contrast, verbs ending in -mit /mɪt/ regularly produce adjectives ending in -issive /mɪsɪv/, with a double s to keep the i vowel “short”.
Both the OED and the OALD agree with this.
I’m thinking therefore that the “other” pronunciation is less broadly accepted, perhaps a regionalism or sort of hypercorrection due to interference with divisible /dɪˈvɪzɪbəl/.
It certainly sounds odd to my own ear.