I got an offer from a company. They asked me to sign the offer as acceptance and send it in 24 hours. It had the compensation, role, probation period and the evaluation process after probation. I signed it and sent them back. But there wasn't any mention on the notice period of the company in the offer. As I thought it will be less positive to ask about the notice period as per Is it okay to ask the notice period of future employer I was waiting to read employment contract. The offer noted that all other details will be included in the employment contract.
Hence I asked them for the contract and salary split up. They sent me the salary split up. But I haven't received my contract details yet. When I checked back with the concerned person the reply was that I will get my employment contract when I join the company as discussed and hence will sign it on the joining date. But I don't remember having the discussion. I am a little concerned that I might end up with a higher notice period but the person says that I will get the contract on the joining date and I don't want to risk anything on the last minute. Also I don't want to make the employer to have a negative impression on the offered role by asking it directly. I am already serving my notice period with my current employer. How should I proceed further on this?