Muslims were taking a break from evening prayers in Finsbury Park, north London, when a man drove a van into the crowd on Monday, injuring 11 people before being apprehended.
The police searched Osborne's home close to the Cardiff golf club in the northeast of the city suburbs.
The victims were all Muslims and the incident was declared a terror attack on the Muslim population.
He said: "If this mosque is attacked, if a synagogue is attacked, if any person is attacked, we are all under attack because of it".
The victims had just enjoyed a meal to signal the end of their fast during the holy month of Ramadan.
"This was an attack on Muslims near their place of worship", she said in a televised address.
A man who had been taken ill before the attack died at the scene. That man later died.
"He is a man of peace and his call for calm, respected by those around him, was inspirational".
Osborne, who lived in Cardiff, had been held down by a group of people after the crash.
She said: "Oh God... you just can't imagine". Hours after the London attack, a man in Paris drove his auto into a police auto; only the attacker died, but it underscored the difficulty of defending against violence by vehicle. If I ever needed anything he would come.
During Monday's attack, witnesses described hearing the assailant shout: "I am going to kill Muslims!"
"The mosque and all the community here admire your support and solidarity". "We saw that clearly after London Bridge", he said. The previous attacks had been blamed on supporters of Islamist extremism.
Osborne's family said they are devastated at the "madness" of the attack.
"We're like Muslims next door to him".
Ali Habib, a 23-year-old student, said residents are angry that the mosque attack hasn't been portrayed in the same light as other attacks across Britain.
The attack is the latest in a series of recent terror attacks in the United Kingdom. Police haven't yet identified the suspect.
Despite the change in leadership and the focus on bolstering inter-faith relations, the mosque reported it had received a string of threatening emails and letters in the wake of the Paris attacks.
"Diverse, welcoming, vibrant, compassionate, confident and determined never to give in to hate". These are the values that will prevail'. It has not been associated with radical views for more than a decade.
Both Theresa May and Jeremy Corbyn were at the scene of Monday.
It was the same tactic Islamic extremists used in recent assaults on Westminster Bridge and London Bridge. The suspect was shot dead by police.
In March London was hit with another auto and knife rampage, that one near parliament. He was also killed by police. Five people were killed in that attack.
"My son is no terrorist - he's just a man with problems and I don't know how to cope with all this", she told The Sun.