I was looking for solution of this issue and I found it. CDS API provide backwards compatibility. The problem is that a result of data is now in netcdf4 format (previous was in netcdf3). Here is description of changes made (not only time dimension name but also order of dimensions was changed):
https://confluence.ecmwf.int/display/CKB/GRIB+to+netCDF+conversion+on+new+CDS+and+ADS+systems
Summarising - if you would like to use previous netcdf format you will able to put
"data_format": "netcdf_legacy"
as a format parameter in your request.
I tried, tested and it works. I know it is deprecated format and it could be outdated in future but for now it solves my problems