I’m currently doing IMT training

I’m currently doing IMT training. I did some locum shifts as bank staff for the trust U.K. currently rotating in.
I just realised the HMRC changed my tax code from 1250L to 1059LX (for my employment with leas employer) and added my locum bank job as a second job with code BR and estimated pay of £5600 annually.
Is that correct or do I need to speak to them to correct tax codes?

Don’t worry. Its normal way of tax code adjustment by the HMRC. At the end of the financial year they will calculate your total and taxable income and depending on the amount of tax you owe, HMRC would adjust it accordingly, ie, they will return you the excess money or will take from your salary.