Solved – Relationship between test stat and p-value in relation to t-test

I suppose this depends on what is meant by "exceed", but generally when people say a test statistics exceeds the critical value, they mean $|t|boldsymbol{>}t_{rm crit}$, and when they say the p-value exceeds the level of significance, they mean $pboldsymbol{<}alpha$. Thus, when the test statistic exceeds the critical value of t, the p-value also exceeds the level of significance.

As to why that fact is the case, it is simply because the value of $t_{rm crit}$ is determined by the point where $p<alpha$.