When buying separate tickets, there is no obligation on the part of the airline to protect you on the next flight, even if both are on the same airline. Some airlines do provide protection across their own network, but this is not automatic and usually a gesture of goodwill on their part.

Perhaps someone with more experience than myself on CX can confirm how strict CX is in these cases, but I would not rely on that.

My suggestion would be to build in a longer stopover or perhaps invest in a good trip disruption insurance policy.