Maybe the sympathomimetic effect in hyperthyroidism which can lead to tachycardia and hypertension.

Ephedrine and pseudoephedrine are adrenergic medications and thyroid hormones have mainly a Betamimetic effect specially in the heart. The pharmacological combination of both may cause palpitations and cardiac arrhythmias. The vasoconstriction is in the peripheral vascular system. In the splacnic vascular system and in the bronchial tree they have the opposite effect (vasodilation and Broncodilation).

Maybe the sympathomimetic effect in hyperthyroidism which can lead to tachycardia and hypertension.

One of the theories: Precipitation of thyroid storm by adrenergic receptor activation. Sympathetic nerves innervate the thyroid gland, and catecholamines stimulate TH synthesis. In turn, increased THs increase the density of beta-adrenergic receptors, thereby enhancing the effect of catecholamines. The dramatic response of thyroid storm to beta-blockers and the precipitation of thyroid storm after accidental ingestion of adrenergic drugs such as pseudoephedrine support this theory. This theory also explains normal or low plasma levels and urinary excretion rates of catecholamines. However, it does not explain why beta-blockers fail to decrease TH levels in thyrotoxicosis.

Hope that answers your question.

Active thyrotoxicisis especially without treatment coupled with the adrenergic effects of ephedrine can bring havoc by un leaching a thyroid storm.

Many manifestations of thyrotoxicosis resemble sympathetic nervous system overactivity especially in cvs , possible explanation include increase number of beta receptor or increase amplification of beta  receptor signal.                                  . Ephedrine is non catechol   phenylisopropylamine so has high bioavailability  and long duration of action and  pseudo ephedrine  is one of four ephedrine enantiomers  , so these drugs can precipitate thyrotoxicosis  and lead to thyrotoxic crisis. 

Because of their potential synergic action with thyroid hormones... I learnt it when I was 2 or 3 year student in Uni)) It was simple quistion)

Possibly a  cellular sensitivity to either catecholamines or thyroid hormone. Ingestion of sympathomimetic drugs in thyrotoxic individuals may precipitate thyroid storm.

TSH release is stimulated by alpha-adrenergic signaling and inhibited with alpha-adrenergic blockers.  This may confuse clinical evaluation of hypo or hyperthyroidism.

Possible explanation, due to sympathetic stimulation. In one study ( animal model) it was demonstrated that sympathetic stimulation induces endocytosis of thyroglobulin and a further release of thyroid hormone meaning they may worsen hyperthyroidism.

It can lead to adrenergic crises, as T3 and T4 produced from thyroid sensitizes the body to catecholamines