Does an IC package type have same dimensions regardless of who manufactures it?
Unfortunately there's a multitude of different variations for pin pitches and package sizes, thermal pad geometries and so on that can make packages incompatible. For a similarly named LQFP or QFN package, for example, the pin pitch might be 0.3, 0.4, 0.5, 0.65 or 0.8 millimeters and the outline of the plastic could be, for example 7x7, 10x10 or 12x12 millimeters. 

Below is an example of one of many pages of dimensions describing various LQFP variants from a single chip packager:


So there are a lot of variants. Also you must take into account the different thermal pad layout requirements for different ICs. It saves a lot of trouble to include the thermal pad layout in a package rather than expect the user to dig through datasheets to get it right. 

But if you get the dimension variant correct, e.g. LFQP52 at 10x10 package, with pitch of 0.65 mm, then I guess it doesn't matter which factory makes the chip.. the pins should be all center aligned, for example.