ok..... one wrong turn but now...
1900 US Census
Frank and Annie Austicon with Frank Jr. in Worcester, MA. He born in August 1869, she in May 1879. Frank (Jr) born Oct 1899 in Massachusetts. Frank and Annie are born in "Poland Russ" on the sheets. There are enough correlations here to believe it's your family. Frank is a carpenter.
Assuming this is your target family, we are now closer to the actual immigration event, we see Frank puts down he came to the US in 1893 and has been in US for 6 years while Annie came in 1898 and has been in US for 2 years.
So we push back when Frank came to the US
Using the gold form at stevemorse.org..... I see some that might fit some of the information:
Stefan Austikalius age 21 from Russia, Kovno, coming into the US on May 20, 1892 on the Scandia from Hamburg. Into NY
On Ancestry.... Alex Austikalnis arriving May 26, 1892 on the Moravia. He is born about 1868. Into NY