Firslty, I advice you to put up a written representation to the company regarding the rectification of the same.
Secondly, if they deny to do the same then you may also go before the labour court for the rectification of the same giving all the details of your joining with another company in August.
Thirdly, but yes you rightly said that they might ask you for the salary in lieu of not serving the notice period.
But yes first get it rectified then would give answer to them for not serving the notice period after knowing some points from your side, so that same can be used against them.
Rest you are welcome to take any assistance in future.