it is correct that the new residence requirement will be phased in over 3 years starting from January 1, 2019.
In 2019 the requirement says that you must have stayed in Denmark for at least 5 out of the last 12 years.
So if you apply for Unemployment benefits after may 2019 and until December 31, 2019 you will meet this requirement.
From january 1, 2020 the requirement will be 6 out of the last 12 years. So also here the same applies: if you apply for Unemployment benefits after May 2020 and until December 31, 2020, you will meet the requirement.
However be aware that because you are a non-EU citizen you also need a work permit that allows you to work full time in Denmark, also after your current jobs ends.
So it is only relevant for you to consider A-kasse membership, if you have a work permit that IS NOT limited to your current job. You need to have a type of VISA/work-permit that is not limited to a specific job.
You also need to meet the general requirements for being eligible for Unemployment benefits, you can read more about the general requirements here:
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