The pronunciation of the word 'tablet' as I found in Oxford dictionary is: [ˈtæblət] While Google say this: ˈtablɪt. Which one is correct?
Which one you use depends on which dialect you're using.
For American English (my dialect), I also think that /tæblɪt/ is an acceptable pronunciation, where the last syllable can be pronounced the same way as the word "lit".
Either is acceptable. This is part of a more general phenomenon: it's not essential to distinguish [ɪ] from [ə] before a consonant in a fully unstressed syllable. Many native speakers don't make this distinction; I think it's more common in British English than in American English, but even British English speakers don't all show the exact same patterns of usage.
The use of "æ" vs. "a" is simply a difference in transcription conventions. They represent the same vowel "phoneme".