Does the test set has to be in [0,1] range?
Standardization centers the values around a mean of $0$ with standard deviation $1$. Therefore, having values smaller than $0$ or greater than $1$ is to be expected. If you want to make sure values are between $0$ and $1$ you need to normalize the data instead.
Here is an example of the two procedures taken from the book &quot;Python Machine Learning&quot; by Raschka:

Be aware though to apply the procedure to your test data with parameters obtained from the training data (in case of standardization: mean and std. dev. of train data).
Sklearn has methods for standardization and normalization which you might want to have a look at.