How to properly restore database from file groups backups?
The sequence may be a bit off for a piecemeal restore you're attempting, in particular when to apply the tlogs. This is what TechNet has documented.


  Piecemeal Restore Under the Full Recovery Model
  
  Under the full recovery model or bulk-logged recovery model, piecemeal
  restore is available for any database that contains multiple
  filegroups and you can restore a database to any point in time. The
  restore sequences of a piecemeal restore behave as follows: 
  
  •Partial-restore sequence
  
  The partial restore sequence restores the primary filegroup and,
  optionally, some of the secondary filegroups. 
  
  The first RESTORE DATABASE statement must do the following: 
  
  ◦Specify the PARTIAL option. This indicates the start of a piecemeal
  restore. 
  
  ◦Use any full database backup that contains the primary filegroup. The
  common practice is to start a partial restore sequence by restoring a
  partial backup.
  
  ◦To restore to a specific point in time, you must specify the time in
  the partial restore sequence. Every successive step of the restore
  sequence must specify the same point in time.
  
  •Filegroup-restore sequences bring additional filegroups online to a
  point consistent with the database.