I was once speaking to my sister on the subject of teaching adult students and she suggested that it must be a good idea to speak with them in Korean where possible. I felt that she didn't really understand the situation or why that might not be a great idea.
At that time I was twenty – two and I was teaching seven students, six of whom were older than me, so my paramount interest was in keeping a sense in the classroom that I was the central focus and the teacher who was meant to be in charge. At that time I also had very little Korean that I could use in the classroom anyway, so everything was conducted in English, or as much as was possible.
In that situation it made a lot of sense to avoid the use of Korean as it would have weakened the classroom experience for everyone. A lot of other times it makes more sense though. As students hear Korean all of the time, and your job is to speak English as much as possible, this might sound counterproductive, but actually explaining Korean words or phrases can be helpful. It is good to show students that they can't get away with saying whatever they want, because you understand them, and it can also be good to help students with translations when they have forgotten something – it's better than allowing them to use their phones to find the answers anyway.
It can be a good way to engage students sometimes, and to show that you struggle to learn Korean just as they can often struggle to learn English. It does a good job of showing that you can try and fail at speaking a language just as they can. It also might alleviate some of the tension created by the fact that you are often speaking in a language some of them might only half grasp sometimes.
On the other hand, Korean and English are such different languages, with very different syntax and grammar, that it can be good to speak in English in order to help them rewire the way they think about the relationship between the two languages. You cannot apply the same rules or even use the same sounds in English, and it is worth showing that what works in Korean often does not work at all in English – the best way to show that is through English.
Parents invariably want their children to be exposed to English as much as possible too, so even though the students might not entirely grasp what it is they are being told – they are at least hearing the rhythm and the tone of English and moving away from the Korean pronunciation which they hear most of the time; this can only be a good thing for learners. Their time with native speakers of the language is generally much shorter than it is with teachers who speak Korean too – so this time can be seen as a useful resource for students to pick up the correct pronunciation of words, and have things corrected by somebody who can provide a definite answer.
Using Korean in the classroom can very often depend on the context, there is a lot of evidence to suggest that low level students gain the least from interaction with native speakers, so trying to pepper conversations with Korean can prove to be very useful for those who are just trying to gain a foothold in the language. There is no benefit to scaring students before they have even begun to learn. As students progress, however, it is often better to keep using English wherever possible because that allows students to fill in the gaps in their understanding without reverting to Korean all the time. There is a lot of evidence that students who are already of a high level benefit the most from hearing more English in English lessons and those who are of a lower level need more Korean to help them to keep up with things.
So the answer to how much Korean you should use is that it depends but that generally it is a good idea. It is probably not a good idea to just use your students as a free Korean learning resource but it certainly doesn't hurt most of the time to use Korean and English to communicate things.