The 300,000 estimate was just for Ireland. Millions died in other countries. It is believed to be responsible also for the cholera epidemic which began in the Bay of Bengal area, spread to Russia and to Western Europe and then to the US. President James K. Polk died in 1849 of cholera, possibly of a strain that went back to the cholera epidemic spawned by the eruption of Tambora.
Watched a special a few months ago about eruptions.
In abt 537 AD, there were two eruptions that really caused problems worldwide. They could not find the source of the eruptions for years and one geologist finally tracked down to, I think, Central America.