There is another designation being used for an interior designer - interior architect.
In a conventional arrangement, a interior designer is engaged by a client to be the consultant for a project. He comes up with the conceptual sketches for an interior. When the design is accepted by a client, he proceeds do draw up the blueprints for construction. Based on the blueprints and specifications, the job is tendered out. The job is awarded to a builder with the most competitive bid. The builder carries out the construction work under the supervision of the interior designer. This arrangement is preferred as the designer and builder are different parties which allows effective supervision and control on the quality of work.
There is the other arrangement where the interior designer offers a 'design-and-build' package' where the designing, consultancy, supervision and construction is done by the same company for a lump sum. This is what TS is providing - designing and execution of a design. Execution does not sound good of course. You don't normally say you 'install interior works'. The physical work carried out is construction. Installation is applied to parts and components such as cabinets, built-in furniture, fittings, finishes, electrical installations etc. You don't normally say you install the structure, the walls and floors. You build them.