AlwaysOn Secondary Replica DB-size
.mdf and .ldf files do not show the last modification date in the way you think it does. 

The file-system date reflects the last time the instance started the database.  Modifications to data continue while the instance has the database open, without the instance actually updating the file-system dates for the files in use by the database.

Can you add the output of sp_helpdb 'dbname' for both instances to your question?  Also add output from:

SELECT d.name
    , mf.name
    , mf.type_desc
    , mf.size * 8192E0 / 1048576 AS FileSizeMB
    , mf.state_desc, mf.max_size * 8192E0 / 1048576 AS MaxFileSizeMB
    , mf.growth  * 8192E0 / 1048576 AS FileGrowthMB
FROM master.sys.databases d
    INNER JOIN master.sys.master_files mf ON d.database_id = mf.database_id
WHERE d.name = 'dbname';


The following query, when run from the database in question, will show the number of megabytes allocated and used:

SELECT sum(total_pages) * 8192E0 / 1048576 as TotalMB
    , sum(used_pages) * 8192E0 / 1048576 as UsedMB
FROM sys.allocation_units;