Welcome to the Airtable community!
You need a different nesting to you formula.
IF(
{Tier} = 1,
DATEADD({Event start}, -4, 'month'),
IF(
{Tier} = 2,
DATEADD({Event start}, -3, 'month')
))
There are many ways to do things in code. Here is another option.
DATEADD(
{Event start},
SWITCH( {Tier},
1, -4,
2, -3
),
'month'
)