The 19th century Manx equivalent of seaworld was at the end of Groudle Glen but think this was late 1890's to WW1 and although I have photos of sea-lions no penguins that I recall.
Another possibility was the aquarium in Douglas (later the Douglas baths) same building as Grand hotel and Theatre at promenade end of Victoria Street - short lived I think and dating c.1880's

Photos in 1880's were not cheap so story sounds a little strange