But says that controls at EU external borders will remain until 15 June

Germany
  • Controls can be reimposed if there are new outbreaks
  • German states should lift quarantine requirements for EU visitors
  • But keep them in place for visitors from outside of EU
  • It is too early to ease border controls with Italy

France and Austria have both maintained that their borders will remain closed until mid-June, so I would reckon this means entry into Germany is allowed but entry from Germany is not allowed during this period.

As for the quarantine requirements, I would assume the German interior ministry is referring to once international borders open back up next month.

It is going to be tough to keep up with the situation across Europe in the coming weeks/months, when you have many countries with different stances on easing of restrictions and border controls - yet there will be free movement in between the region for citizens.