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QUESTION
We have a customer who intends to install porcelain tile on interior and exterior floors. The movement joint width they are considering is 3/16". The depth will be 3/8" (tile thickness). We have two questions
  1. Considering this depth, is it necessary to use a backer rod?
  2. If the contractor does not use a backer rod, is there any risk of 3-sided adhesion?
ANSWER You will find the answers to your questions in the 2024 TCNA Handbook (page 438-445) EJ171. Materials are listed as follows: “Backup strip shall be a flexible and compressible type of closed cell foam polyethylene, butyl rubber, or open cell and closed cell polyurethane, rounded at the surface to connect sealant, as shown in the details, and as recommended by sealant manufacturer. It must fit neatly into the joint to such a height to allow a sealant depth of half the width of the joint. Sealant must not bond to the backup material.”
Please see pages 442-445 for details of different types of movement joints.
All of the details shown have a rounded backup strip, bond breaker tape, compressible backup or filler strip. These are all used to prevent three-sided adhesion.
Backer rod and sealant use are covered in the TCNA Handbook chapter “EJ171 Movement Joint Guidelines for Ceramic, Glass and Stone.”
You mentioned the customer is considering a 3/16" joint width; on what basis are they considering that width? I would question if that width and depth are adequate to meet the demands of the material and the installation environment it’s located in and the structure it is installed on. 
The second paragraph of EJ171 states “Because of the limitless conditions and structural systems on which tile can be installed, the design professional or engineer shall show the specific locations and details of movement joints drawings. Preparation of openings left by the tile contractor and installation of backup strip and sealant should be specified in the caulking and sealant section of the job specifications.” 
In other words, it is not the tile contractor’s responsibility to determine the placement or the width/depth of the movement joint. This calculation should be done by a design professional (architect or engineer) and specified in writing after considering the environment, material, substrate, conditions, etc., of the tile assembly.
I would recommend you take a look at EJ171 in your TCNA Handbook for more information about backer rod, sealant, and movement joints.