A rotten egg smell from the tap is unpleasant and easy to misplace. The odor is hydrogen sulfide gas. It can come from the water supply, from bacteria living in parts of the system, or from a reaction inside the water heater. Each cause has a different fix, so find out which one you are dealing with before you call a company or buy anything.
Check whether the smell is hot water only
Run the cold tap at the kitchen sink and smell it, then run the hot tap at the same sink and smell that. If only the hot water smells, the most common cause is the water heater, not the softener. Some water heaters with magnesium or aluminum anode rods can produce hydrogen sulfide when sulfate in the water feeds bacteria inside the tank. A standard softener does not fix this, so it is not the place to start. Ask a plumber to inspect the anode rod and the tank first.
Check the cold water and the source
If the cold tap smells too, the smell is either arriving with the water or being added somewhere between the supply and the tap. On a private well, ask for a water test that includes hydrogen sulfide, sulfate, and bacteria. On a municipal supply, look at the utility's water quality report and call the utility if the smell is sudden or affects only your home. Keep any test results with your other water records so they are easy to compare later.
Look at the softener itself
Open the brine tank and smell the water and the salt. A sour, sewage-like odor in the brine tank, or slime on the tank walls, suggests bacteria are growing in the system. Resin beds can harbor bacteria, especially when the unit has sat idle for a long stretch, such as a long vacation, or when the brine tank has been allowed to run low. Also note whether the smell is strongest right after a regeneration, since that cycle can push water from the brine and resin area into the lines.
Questions to put to the installer or service company
Ask whether they will sanitize the resin bed, what product they use, and whether the cleaning follows the manufacturer's instructions. Ask whether the unit has a sanitizing cycle, how often it should run, and who sets it up. Ask whether they will test your water before and after the cleaning and what result would count as a fix. Get the answers in writing. If the company offers a fix without a test, get a second opinion before you agree to the work or to a larger system.
What to do while you sort it out
Until the cause is known, avoid using the hot tap for drinking or cooking if the smell is strong, and run the cold tap for a minute before using it if the smell is present. Leave the water heater settings as they are unless a plumber advises a change. Keep a short log of when the smell shows up, which taps it comes from, and whether it follows a regeneration, so the person who diagnoses the problem has something concrete to work from.
When the smell stays after the cleaning
If the smell returns after the softener has been cleaned and the water heater has been checked, the likely cause is the source water, and a softener alone is not the right answer. Get the source tested before you buy another softener or agree to a bigger system. A company that can explain what the test found, and how the treatment you are considering would address it, is worth more than one that only offers to replace the unit.