Settlement of Option assignment does not depend on current mkt premium/price of option.It uses the strike price and End of Day settlment price (which is generally the daily closing price of the underlying stock).
So when call holder of 100 strike price, excercises his rights to buy the stock at 100 Rs., the seller has obligation to give him stocks at 100 Rs. If he already has stocks in DMAT then it can paid directly. Else, he has to buy underlying stocks from mkt by paying CMP of 105 and give it to option buyer at 100 rs. and taking loss of 5 Rs.
Question is - will the call holder excercise his 100 strike option when CMP is 105. Because he has already 10rs for this call, then it makes sense for him to excercise only when CMP goes above 110. He would be better off sqauaring off the option at 12 and book profit of 2 Rs. rather then taking the delivery at 100 rs.
In general, if option CMP has any time value in it, it is better to square off the option and collect time permium that mkt is giving to that option. Excercise makes sense only when there is no more time premium left. (eg. in above example 105 option selling at 12, has 5 rs of real value and 7 rs of time value. Only a novice trader will make a mistake of loosing that 7rs of time value and excercise this option.).
In India, option excercise is Cash settled so there will be only debit/credit entries in your acct. It doesn't require any DMAT transaction. In US mkt, you would see the stocks entry in your trading acct as a result of option excercise/ assignment.
Another important factor comes is the type of option - American or European. American types of options can be excercised anytime but European option can be excercised only on expiry date.
Happy Trading