Partitioning never places specific partitions of the data on specific files UNLESS you have multiple filegroups - the files that make up a file group have a proportional fill algorithm on where the data is located.
For Managed Instance - you can ONLY have the PRIMARY file group - but for performance you can have many files under this.
With partitioning, the partition elimination will still work with Managed Instance and the optimiser will create a plan that eliminates partitions in the same way SQL Server does. In the same way that SQL Server does, it can also generate a parallel plan that will assign threads to each partition. But this is the SAME as SQL Server - so if you achieved it with your specific tables, data and queries then you should be able to achieve the same with Managed Instance