It is correct. one can pray voluntary prayers until the Imam comes out. As for the interval between the two athans, this is wrong. It should be longer than that so that people would prepare for the prayer.

I was in saudi arabia couple of years back and during friday prayer they gave just around 2 minutes break in between two adhans.when i inquired about this they told that there is no forbidden times for prayer on fridays and we can pray the sunnah prayer