You are binding your DNA/RNA to beads and washing them to remove contaminants like proteins and lipids. In the final plate you are releasing your DNA/RNA from the beads using the elution buffer. the elution buffer + DNA/RNA is then the eluate.

In DNA/RNA extraction protocols, eluate refers to the final solution that contains the purified DNA/RNA, which is typically obtained by eluting or washing the DNA/RNA from a solid support such as a column, magnetic bead, or filter. The elution buffer is a solution that is specifically designed to release the purified DNA/RNA from the solid support and into the eluate.

Therefore, yes, the DNA/RNA should remain in the eluate after the extraction protocol is complete. In your case, the last plates where you put the elution buffer is likely where the eluate is collected.

Yes there is the presence of DNA/RNA. Its traditionally asked to add RNAse or DNAse whichever is appropriate.