Hi I'm English and I can't help you with the technical structure of the language but I can tell you I don't know anyone at all who would say "it's high time".
It's time you applied for your visa sounds more formal, like it needs to be done and could be said to someone in person or via an email reminder or letter.
It's about time is more used in general conversation with friends or family members, for example if you know your friend has booked a holiday and needs to hurry up and get their visa in place it could be said as a friendly reminder.

I don't know if this helps you at all, I hope it does.

If you want to say them in the past tense I think it would be something like:
Have you applied for your visa?
Did you apply for your visa?
I have applied for my visa.
I applied for my visa on time.
You applied for your visa.

These mean roughly the same thing. Be careful not to say "it's a high time".  Maybe that was just a typo as you used it correctly in the rest of your text.

One of these cases can be a little tricky and mean something else.

This example is a reminder: "It's about time to renew your visa."

This example is an exasperated remark (i.e. you're kind of mad/shocked): "It's about time you renewed your visa!". The words in bold are said with emphasis and you are probably shaking your head and glaring at the person. The phrase basically means "Well, you finally decided to get around to renewing your visa like you should have done a long time ago". Something you might say to your spouse when you have a big trip planned coming up soon and they were procrastinating getting their visa.

As for using "it's high time", well that's not too common for me, but not unheard of either. Like Alex said, some places like to use it more.

It’s time to do ---> I often used it in an "upcoming" incident to remind someone to do.
"I think it is time for us to leave for the museum" (we are leaving in a short time)

In the past, I would say:
I thought that was time for us to leave for the museum. 

In your case, about visa application:
I thought you should have applied for the visa. (not finished yet) 
I thought you had applied for the visa (finished)

Personal knowledge. Hope that can help you. 

It's time to do something (you wouldn't use high/about with this) is for something that should be done now. It is something that is on time or scheduled.

"It's time to set off for now"

It's about time you did something is for something that is late and mayne you should have done before.

"It's about time you set off; you are late".