I think that the partnership firm mentioned might be an "establishment" coming under the purview of the State Shops and Establishments Act relating to service conditions of its employees and its location must be Bengaluru. If so, the employees should be allowed a weekly holiday of at least one whole day for rest as per sec.12(3) and no deduction should be made from the wages of the employees including a daily wager on account of the given holiday as per sec.12(5) of the Karnataka Shops and Commercial Establishments Act,1961.
The contention of the manager is not correct in view of the provisions of annual leave with wages @ one day for every 20 days of service rendered and sick leave @ 12 days per year as per sec.15(1) and(3) of the Act respectively.
If the poster actually informed about his leave and got it sanctioned even orally, the employer can not deduct wages.