Preponement of Relieving Date
Simple answer - No.
Preponement of your relieving date is not deemed to be 'termination' from the employer's side. There are various business factors attached to an early release of an employee, such as the position becoming financially unviable, no projects or work coming in the near future, high billable costs for you, or an employee not performing well in the initial few days or months. It could be anything.
Notice Period During Probation
Also, please see if you have served the notice period applicable to your probation period. There has to be a notice period; it is written in those lengthy offer letters. Typically, it ranges from 2-6 weeks during a probation period.
Practical Advice
Please obtain written proof that the employer is releasing you earlier and "it is not you who is wanting to leave immediately" or say "you are ready to serve the applicable notice period as per the employment offer." This is important because there are unprofessional practices in place these days by many employers and unscrupulous HR. They may release you early but demand payment for the unserved notice period and put the blame on you for not serving the full notice period, making you pay a hefty amount through threatening legal action.
Other than that, there should not be any worry.
All the best for your new job.