Since I don't grow Kentucky blue grass, I cannot say anything about what it should look like.
If you are using a rotary mower it tears the blade like a weed whacker. A power reel mower is more expensive but is better for the grass blades because it cuts more like a knife. You still need a sharp mower.
It sounds like you mowed it correctly. Never cut off more than 1/3 of the blade at a time.
Insects can cause brown tips but since this occurred after mowing it may be from that. As a test hand clip a small section of the grass with sharp shears mainly to cut off the brown tips. If the brown tips do not come back it is probably from the mower.
Your type of grass is prone to fungal diseases. Test your watering. You should be putting down about an inch a week of water by sprinkler or in rain. Set out tuna cans at 2 ft intervals turn on the sprinkler and time how long it takes to fill the cans. That would be how long you have to water to put down and inch of water. I divide the time in two and water on Tuesdays and Fridays. I also have a rain guage to tell me how much it rained. It is a handy thing to have. Many times it seems like it rained but it barely got the rain guage wet.
Check your soil drainage. You can do a drainage test but since the grass is already in, you just need to dig down and see how deeply watered the soil is after you water. Wait a few days and dig another hole to see how moist it is. the top dries out faster than the deeper soil, so you want to know how moist it is about 4 inches down. The purpose of long deep watering is to encourage the roots to go deep where the moisture is. If you only water for 10 minutes a day the roots will stay shallow and the soil will dry out quickly and the grass will be less drought tolerant and dry out faster. Grass needs to get the right amount of water or you will see drying and dying especially if the lawn is not established yet.
On the other hand if your soil drains poorly, you will need to adjust watering to give the soil time to dry out otherwise you will have more issues with fungus. Fungal problems can occur as brown spots usually in the low spots in the lawn or as an expanding brown ring (fairy rings). If after a heavy rain you see the mushroom appearing on the lawn then you know what that is from. Fungus in the lawn is not necessarily a bad thing. Usually they are there to consume the decaying matter. If there is a lot of it then it is usually because the grass roots are dying for some reason.
The other things that commonly can cause grass tips to brown and brown spots are lawn grubs. Fast growing grasses with soft blades are more susceptible than a tougher grass like zoysia in warm climates. If you have Japanese beetles, milky spore should be applied in the fall when the grubs are active. It needs to be applied in patches and should help control Japanese beetle grubs in the future. There are other products available to control other kinds of grubs, but you want to make sure that is the problem first. Check out the Michigan link.
https://web.extension.illinois.edu/blmp/ ... 27553.html
https://msue.anr.msu.edu/news/how_to_cho ... _your_lawn
https://www.extension.umn.edu/garden/ins ... e-beetles/
Happy gardening in Hawaii. Gardens are where people grow.