This is because of the incorrect upsized tyres. You are using 165/70 R13 where as the recommend upsize is 165/65 R13. This effectively means your tyre's sidewall height is 8.25 mm extra than recommended. This is the prime reason for the tyres touching the wheel arches.
I suggest you try tyres of 165/65 R13 size. If the problem still persists then there is some issue with the shockers. But I believe correct tyre size would solve the issue.