I'm going to guess you are overwatering.

Where do you live?

What kind of grass do you have?

What is your watering schedule? How often and for how long do you water?

I live in Sydney, Australia.

Was told the grass is Empire Zoysia, supposedly a type of buffalo.

During summer it was watered almost every day that was hot, using sprinklers for about 30 minutes.

Zoysia is its own type of grass. Buffalo, even on Oz, is different.

You were, and likely still are, watering wrong. That's what the grass will look like when you water too frequently and not deep enough. Pictures to follow. Here's more info about watering.

Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 3 cm all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps from 33-38 deep water once per week. With temps from 25-32 deep water once every 2 weeks. With temps from 21-24 deep water once every 3 weeks. With temps below 21, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. In the USA this deep and infrequent schedule works in Phoenix and in Vermont (for Oz think Hobart to Darwin including Alice Springs), so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

And here's the motivation for proper watering:

Thanks to morpheuspa for posting this pic many years ago. All the lawns in the neighborhood are Kentucky bluegrass. All of morph's neighbors water daily. Morph waters deeply and infrequently based on the paragraph above. Use that paragraph as a guideline to get the lawn fixed. Then tune it up for your specifics. There are other factors which play into this. Air temp is 90% of it, but there is also soil type, grass type, humidity, cloudiness, wind, grass mowing height, and a few more. But start with the daytime high temp and don't overthink it with all the other factors.

Here's another picture you might be interested in.

This one was posted by mrmumbles many years ago. The grass is zoysia like yours. The fertilizer he used was alfalfa pellets (rabbit chow). He tossed a handful in mid May (late spring) and took the picture in mid June. You can clearly see the improved color, density, and growth. Alfalfa is a common ingredient in organic lawn fertilizers. We like to skip the high prices and just buy animal feed like soybean meal, alfalfa meal/pellets, corn meal, or any other ground up nut bean or seed. The application rate is the same for all of them at 8 kilos per 100 square meters. You should be able to find something in 20 kilo bags at your local feed store.