I can say right away that you are really lucky to be working in such an organization that credits your last month's salary even after resigning, and that too after giving a clear unilateral deadline of moving out. Please go through the many threads/postings in CiteHR, and you will know what this means. It directly points to the culture prevalent in this company—a very positive one that says, by action and not just words, "WE TRUST YOU & EXPECT TO BE TRUSTED TOO."
Notice Period and Resignation
Coming to your resignation, what's your notice period as per the HR policies? Many companies have some notice period even during probation, albeit a lower period. And, to add, frankly, irrespective of the notice period duration, one can't give any unilateral deadline that contravenes the notice period guidelines/policies—it's for both the individual and the company to arrive at that timeline through discussion in such situations.
If you read the many threads/postings in CiteHR, you will realize that many companies, including MNCs, just play around (at the least) or harass the employee without relieving. The last month's salary is out anyway.
Consider Staying with the Company
At the risk of being objected to, of interfering in your career steps, I would suggest you have a relook at your resignation and discuss with your manager and HR about staying back—you can possibly ask for a hike to do it, to cover the rise you may be getting by joining the other company. Any company where such a positive culture exists is worth working for—if need be, with a few compromises along the way.
All the best.
Regards,
TS