Table partitioning for cloud service?

I’m working on my first cloud service, which will be backed by a postgresql database. Currently I only have a single customer, but of course I want to design with the possibility of multiple customers in mind. In that vein, I’m wondering what is “typical” in terms of designing the DB structure to make sure that one customer doesn’t “accidentally" get data for another customer? At the moment I am leaning towards giving each customer their own set of tables, with a unique prefix for each. This would provide a “hard” separation for the data, but would also increase maintenance efforts, as if I needed to add a field I would have to add it to every table. On the other hand, keeping everything in the same set of tables would mean having to be VERY careful with my SQL to make sure no customer could access another’s data.