Can not route back to list of records with filters when use startProcessLink to start interface

Where does it takes you when you click on the "Yes" button?

it return record list initial

You cannot hold the filter values. They'll go blank again but here is a workaround. 

1. Build this record list in an interface using source of the grid as record. 
2. Do not use the default search rather build a custom search by using a!textField()
3. Store the entered value in the Appian's cache memory using the textCahce plugin and when returning back to the record list, get the cache value and assign it in the same variable.  

If I only need it can back record list  (don't need  to hold filter value) when I click "yes" button. What need I do?

I think it should automatically work. With the screenshots you have attached, it looks like you are trying to achieve it from the designer. Did you try it from the tempo or site? 

I am using site

Let's get the basics clear here. 
Appian's record has 2 different interfaces that we are mixing up here. 

1. Summary Interface
2. Related Action interface. 

You do not need a!startProcessLink to open a summary dashboard. Neither for a record action. But the difference between the two is. 

Summary Dashboard is used when you want to show read-only information to the user about the record on which they have clicked. You can add it to the record itself. No need of a process

Record Action is used to update the record (hence an editable form) which you can add in a process and then add the process to the record again. 

So I don't find a need to use a!startProcessLink() here. 

Let's get the basics clear here. 
Appian's record has 2 different interfaces that we are mixing up here. 

1. Summary Interface
2. Related Action interface. 

You do not need a!startProcessLink to open a summary dashboard. Neither for a record action. But the difference between the two is. 

Summary Dashboard is used when you want to show read-only information to the user about the record on which they have clicked. You can add it to the record itself. No need of a process

Record Action is used to update the record (hence an editable form) which you can add in a process and then add the process to the record again. 

So I don't find a need to use a!startProcessLink() here. 

I agree that a Start Process link doesn't seem necessary here. I'd instead recommend using a Record Action. When you use this, you can configure the action to open in a dialog. Then, after you complete the action it will return you to where you were before (with filters intact).