Your question and details are somewhat confusing. In simple terms, what I understand is that the employee will be taken as a Management Trainee (MT). He/She will be reporting in Bangalore, and after 3 weeks of being in Bangalore, he/she will be sent for Management Training near Pune (you simply mention out of Pune). After successful training, you will be posted out of Bombay at our plant/office/unit as a Management Trainee for a period of ... months.
Here, the specific period is right from the date the person reports in Bangalore will be counted, or after they are sent for training, their start date will be counted as an MT. The person is joining you in Bangalore first, and therefore, he is your employee, whatever position you assign him by designation. As the company is sending him for training, all expenses for travel, accommodation, and food are to your account. Also, if he is directly required to report outside Bombay, then the travel is your company's account.
In other words, if you are directly sending him to report to your training center, then you should reimburse his travel expenses from his house to the training center and return after the training. As the company expects its employees to learn their policy and work ethics through training, it is the company's expense to arrange everything. HR should look beyond the ground level when the company's prestige is represented by your employees.