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Hello Sharks,
I recently gave interview of Tiger Analytics and after all successful technical discussion, they were offering me Senior analytics - data Science role for 15.5 fixed + 2L jb, considering my current yoe 4.3 and in data science relevant is not much but my cctc is 14(13fixed+1 variable), I denied to accept this offer. Should I reconsider that?
Opening in Wipro

I'd definitely give your manager a heads up. It's the courteous thing to do and if he/she is blindsided, it may sour your relationship moving forward if you don't end up getting the other job. Just explain why you're interested in changing roles.
Oh yeah, that is awkward. Why did you take this opportunity if they weren't willing to match the other offer? It sounds like he already knows you're unsatisfied with your pay, so applying for other positions shouldn't surprise him. Just say "Hey, just letting you know I'm interviewing for this other role. Will let you know how it pans out." Don't be too cocky like you expect to get it and it shouldn't be any extra awkward than it already is.
Def let your manager know. Most places actually require you to tell them before you apply. I am surprised that is not the case there.