If you run the following, you will see that the datetime value is implicitly converted to the character string you showed:

declare @TestDate varchar(10) = '01/2013';

select

@TestDate,

stuff(@testDate,3,0,'/01'),

convert(datetime, stuff(@testDate,3,0,'/01'), 101),

cast(convert(datetime, stuff(@testDate,3,0,'/01'), 101) as varchar);