What are the best strategies to deal with multicollinear variables? I have a time-series dataset that has 63 features. The predictions are coming out to be extensively wrong; specifically because of the high collinearity among some of the variables according to this correlation matrix:

My question is how do variables that have collinearity shown as blue squares affect ML models other than the red ones that of course inflate the variance of the response variable and do they need to b treated the same as the red squares?
 A: Whether the correlation is positive or negative has nothing to do with the severity of nor the way you treat colinearity.
Correlation is the extent to which one variable changes when the other does. Colinearity is when two or more variables are a linear combination of one another. 
If there is perfect colinearity, then a variable can be completely explained as a linear combination of other variables. 
Consider the simple example $A=-B$:


*

*These are perfectly negatively correlated;

*$A$ and $B$ are perfectly colinear.


To give an example of three perfectly colinear variables (but not perfectly positively or negatively correlated):
$A+B+C=1$
Adding all three of these variables to a regression model would cause colinearity issues, but this has little to do with their pairwise correlations.
A: From a regression perspective, sever multicollinearity between features can cause your standard errors to become unstable. For continuous features, one usually computes the Pearson correlation and excludes predictors above some prespecified cutoff. There are a number of cutoffs that you can use; there's no hard and fast rule for what value to use as a cutoff. 
For predictive modelling, the variable which is the least predictive is removed. To keep it simple, you could just look at univariate measures of the predictive strength a variable has with the response.  
That said, if predictive performance is your goal (as is generally the case with machine learning), using PCA to condense your predictor set seems like a reasonable idea. I believe the literature you're referring to means the magnitude of the correlation. That is, the absolute value of the Pearson correlation. That's why they never mention 'negative correlation', as you say. 
