Thank you so much!
Yes you first allocate ressources in the district you are currently in and then you move. The thematic idea behind it is that campaigning (such as handing out flyers) takes time. So you move in a new district and then have to spend a week there (getting to know the area) before being able to campaign and only then move to the next disctrict.
Remember this is a 30M people city and each district is huge.
I think it would be weird to move in a new district and instantly be able to campaign.